Each side of an equilateral triangle is increased by $1.5 \%$. The percentage increase in its area is......$\%$

The area of a triangular lawn is $1600 \, m^{2}$. If one side is $64 \, m$ long and the other two sides are equal in length,the length of each equal side is......$m$

$A$ lawn is in the form of a triangle having its base and height in the ratio $2:3$. The area of the lawn is $\frac{1}{12}$ hectare. Find the base and height of the lawn.

In the given figure, $ABCDEF$ is a regular hexagon whose side is $6\, cm$. $APF$, $QAB$, $DCR$, and $DES$ are equilateral triangles. What is the area (in $cm^2$) of the shaded region (in $\sqrt{3}$)?

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?

$A$ sphere of $30 \ cm$ radius is dropped into a cylindrical vessel of $80 \ cm$ diameter,which is partly filled with water. If its level rises by $x \ cm$,find $x$ (in $cm$). (in $.5$)